Chapter I Special relativity and spacetime We might speak of an observer O using frame S,or a different observer O'(read as 'O-prime')using frame S'(read as 'S-prime'). Though you may think of an observer as a person,just like you or me,at rest in their chosen frame of reference,it is important to realize that an observer's location is of no importance for reporting the coordinates of events in special relativity.The position that an observer assigns to an event is the place where it happened.The time that an observer assigns is the time that would be shown on a clock at the site of the event when the event actually happened,and where the clock concerned is part of the network of synchronized clocks always used in that observer's frame of reference.An observer might see the explosion of a distant star tonight,but would report the time of the explosion as the time long ago when the explosion actually occurred,not the time at which the light from the explosion reached the observer's location.To this extent,'seeing'and'observing'are very different processes.It is best to avoid phrases such as 'an observer sees... unless that is what you really mean.An observer measures and observes. Any observer who uses an inertial frame of reference is said to be an inertial observer.Einstein's special theory of relativity is mainly concerned with observations made by inertial observers.That's why it's called special relativity -the term 'special'is used in the sense of'restricted'or 'limited'.We shall not really get away from this limitation until we turn to general relativity in Chapter 4. Exercise 1.I For many purposes,a frame of reference fixed in a laboratory on the Earth provides a good approximation to an inertial frame.However,such a frame is not really an inertial frame.How might its true,non-inertial,nature be revealed experimentally,at least in principle? ■ 1.1.2 The postulates of special relativity Physicists generally treat the laws of physics as though they hold true everywhere and at all times.There is some evidence to support such an assumption,though it is recognized as a hypothesis that might fail under extreme conditions.To the extent that the assumption is true,it does not matter where or when observations are made to test the laws of physics since the time and place of a test of fundamental laws should not have any influence on its outcome. Where and when laws are tested might not influence the outcome,but what about motion?We know that inertial and non-inertial observers will not agree about Newton's first law.But what about different inertial observers in uniform relative motion where one observer moves at constant velocity with respect to the other? A pair of inertial observers would agree about Newton's first law;might they also agree about other laws of physics? It has long been thought that they would at least agree about the laws of mechanics.Even before Newton's laws were formulated,the great Italian physicist Galileo Galilei (1564-1642)pointed out that a traveller on a smoothly moving boat had exactly the same experiences as someone standing on the shore. A ball game could be played on a uniformly moving ship just as well as it could be played on shore.To the early investigators,uniform motion alone appeared to have no detectable consequences as far as the laws of mechanics were concerned. An observer shut up in a sealed box that prevented any observation of the outside 14Chapter 1 Special relativity and spacetime We might speak of an observer O using frame S, or a different observer O % (read as ‘O-prime’) using frame S % (read as ‘S-prime’). Though you may think of an observer as a person, just like you or me, at rest in their chosen frame of reference, it is important to realize that an observer’s location is of no importance for reporting the coordinates of events in special relativity. The position that an observer assigns to an event is the place where it happened. The time that an observer assigns is the time that would be shown on a clock at the site of the event when the event actually happened, and where the clock concerned is part of the network of synchronized clocks always used in that observer’s frame of reference. An observer might see the explosion of a distant star tonight, but would report the time of the explosion as the time long ago when the explosion actually occurred, not the time at which the light from the explosion reached the observer’s location. To this extent, ‘seeing’ and ‘observing’ are very different processes. It is best to avoid phrases such as ‘an observer sees ...’ unless that is what you really mean. An observer measures and observes. Any observer who uses an inertial frame of reference is said to be an inertial observer. Einstein’s special theory of relativity is mainly concerned with observations made by inertial observers. That’s why it’s called special relativity — the term ‘special’ is used in the sense of ‘restricted’ or ‘limited’. We shall not really get away from this limitation until we turn to general relativity in Chapter 4. Exercise 1.1 For many purposes, a frame of reference fixed in a laboratory on the Earth provides a good approximation to an inertial frame. However, such a frame is not really an inertial frame. How might its true, non-inertial, nature be revealed experimentally, at least in principle? ■ 1.1.2 The postulates of special relativity Physicists generally treat the laws of physics as though they hold true everywhere and at all times. There is some evidence to support such an assumption, though it is recognized as a hypothesis that might fail under extreme conditions. To the extent that the assumption is true, it does not matter where or when observations are made to test the laws of physics since the time and place of a test of fundamental laws should not have any influence on its outcome. Where and when laws are tested might not influence the outcome, but what about motion? We know that inertial and non-inertial observers will not agree about Newton’s first law. But what about different inertial observers in uniform relative motion where one observer moves at constant velocity with respect to the other? A pair of inertial observers would agree about Newton’s first law; might they also agree about other laws of physics? It has long been thought that they would at least agree about the laws of mechanics. Even before Newton’s laws were formulated, the great Italian physicist Galileo Galilei (1564–1642) pointed out that a traveller on a smoothly moving boat had exactly the same experiences as someone standing on the shore. A ball game could be played on a uniformly moving ship just as well as it could be played on shore. To the early investigators, uniform motion alone appeared to have no detectable consequences as far as the laws of mechanics were concerned. An observer shut up in a sealed box that prevented any observation of the outside 14